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Unformatted text preview: 650:460 Aerodynamics Quiz No. 4 - Solution
Prof. Doyle Knight Tel: 732 445 4464, Email: [email protected] Oﬃce hours: Tues and Thur, 4:30 pm - 6:00 pm and by appointment Fall 2009 1 Quiz No. 4
A two-dimensional airfoil has a camber line deﬁned by z x =ε c c 1− x c for 0 ≤ x ≤ c where ε = 0.1 is a dimensionless constant. Find the value of cmac . See lecture notes for deﬁnite integrals. Solution The slope of the camber line is d (z /c ) d (x /c ) = ε 1−2 = ε cos θ x c 2 Quiz No. 4
The coeﬃcients in the Fourier series for the vorticity are 2 π dz A1 = cos θ d θ π o dx 2π ε cos2 θ d θ = πo =ε 2 π dz cos 2θ d θ A2 = π o dx =0 using
π cos mθ cos nθ d θ =
o π 2 if m = n and zero otherwise Thus cmac = π π (A2 − A1 ) = − ε 4 4
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This note was uploaded on 12/15/2009 for the course 650 460 taught by Professor Knight during the Spring '09 term at Rutgers.
- Spring '09